# How Bridges Work 5, Exercise 3: how long does a corroding plate last?
# A flat plate 200 mm wide and 12 mm thick carries a steady tension of 240 kN.
# It loses material from both faces at the rate given below (assumed rates, mm
# of thickness lost per face per year). The allowable stress is 165 MPa. Find
# how many years each rate takes to reach that stress, and the stress after
# 50 years. Then suppose paint stops all corrosion for the first 25 years:
# when does the plate reach the limit?

width, thick0, force, allow = 200, 12.0, 240e3, 165

def stress(years, rate):
    return force / (width * (thick0 - 2 * rate * years))

t_min = force / (width * allow)
print("minimum thickness", round(t_min, 2))
for rate in (0.01, 0.05, 0.1):
    years = (thick0 - t_min) / (2 * rate)
    print(rate, round(years, 1), round(stress(50, rate), 1), round(25 + years, 1))

# Output when run:
# minimum thickness 7.27
# 0.01 236.4 109.1 261.4
# 0.05 47.3 171.4 72.3
# 0.1 23.6 600.0 48.6
#
# The plate may be thinned to 7.27 mm before the stress reaches 165 MPa. At 0.01
# mm per face per year that takes 236.4 years, at 0.05 mm 47.3 years and at
# 0.1 mm 23.6 years. After 50 years the stress is 109.1, 171.4 and 600.0 MPa for
# the three rates; the last is far beyond the limit, so the plate would
# already have failed. Paint that stops corrosion for the first 25 years moves
# the limit to 261.4, 72.3 and 48.6 years. The lesson: the corrosion rate is the
# big unknown, the stress rises faster the thinner the plate gets, and
# keeping the coating intact buys years. Real corrosion pits and crevices make
# local thinning worse than this uniform model.